Question:
Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10440
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $10440 – $5800 = $4640
Thus, Simple Interest = $4640
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 4640/5800 × 10
= 464000/58000
= 8 years (using formula)
Thus, Time (T) = 8 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $5800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4640 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 10% of Principal
= 10% of $5800
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = 580
Thus, simple Interest for 1 year = $580
Now,
∵ If the simple Interest is $580, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/580 years
∴ If the simple Interest is $4640, then the time = 1/580 × 4640 years
= 1 × 4640/580 years
= 4640/580 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(4) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(9) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?